Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Triangle {

	public static void main(String [] args) throws Exception{
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();

		HashSet<Integer> trinums = new HashSet<Integer>();
		int i = 1;
		while(true){
			int tri = i*(i+1)/2;
			
			if(tri>n)
				break;
			trinums.add(tri);
			i++;
		}
		boolean ya = false;
		for(int tri : trinums){
			if(trinums.contains(n-tri)){
				ya = true;
				break;
			}
		}
		if(ya)
			System.out.println("YES");
		else
			System.out.println("NO");
	}

}